Free energy model for solid high-pressure phases of carbon

Abstract

Analytic free energy models for three solid high-pressure phases--diamond, body centered cubic phase with eight atoms in the unit cell (BC8), and simple cubic (SC)--are developed using density functional theory. We explicitly include anharmonic effects by performing molecular dynamics simulations and investigate their density and temperature dependence in detail. Anharmonicity in the nuclear motion shifts the phase transitions significantly compared to the harmonic approximation. Furthermore, we apply a thermodynamically constrained correction that brings the equation of state in accordance with diamond anvil cell experiments. The performance of our thermodynamic functions is validated against Hugoniot experiments.

The structure in warm dense carbon

“…Theoretical investigations have been complimentary and are in many ways pioneering as experiments for ultra-high pressures may still be beyond the technical capabilities. We distinguish theories for the equation of state in the high temperature (plasma) regime based on the chemical picture [29][30][31], average atom models [32,33], density functional molecular dynamics (DFT-MD) for the correlated liquid and solid [15,22,[34][35][36][37][38][39][40][41][42][43][44][45][46][47], and DFT for a variety of acknowledged and proposed solid phases [48][49][50][51][52][53][54][55][56][57][58][59]. More exact theories like quantum Monte Carlo are available [60,61] as are classical molecular dynamics simulations employing sophisticated multi-body potentials [62][63][64][65][66].…”

Stochastic density functional theory at finite temperatures

“…The former involves very moderate computational effort but is of limited accuracy due to the use of approximate kinetic energy and entropy functional. The latter class of DFT approaches on the other hand yields reliable and accurate results and is emerging as the method of choice in the field, with applications rangingfrom short pulse laser simulations [35,36] and xray scattering [37,38] to properties of astrophysical bodies [8,[39][40][41].…”

Reflecting laser-driven shocks in diamond in the megabar pressure range

“…For instance, the insulating solid to metallic solid transition predicted in Refs. [6,12,54] is incorporated into the phase diagram proposed by Kerley and Chhabildas [54] and produces a change in slope along the Hugoniot at 4.3-5 Mbar. Similarly, but in the opposite direction, the Hugoniot calculated from SESAME table 7834 ( Figure 7) shows a small kink in the Hugoniot curve at ∼9 Mbar that is not present in SESAME table 7830.…”

“…Later theoretical works (1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999), often based on numerical simulations using ab initio calculations, resulted in establishing a full picture for the phase diagram of carbon [6][7][8][9] . More recently, accurate first-principle multiphase EOSs for carbon at high pressures and temperatures have been established [10][11][12][13] .…”